A Parallel Distance-2 Graph Coloring Algorithm for Distributed Memory Computers (original) (raw)

Abstract

The distance-2 graph coloring problem aims at partitioning the vertex set of a graph into the fewest sets consisting of vertices pairwise at distance greater than two from each other. Application examples include numerical optimization and channel assignment. We present the first distributed-memory heuristic algorithm for this NP-hard problem. Parallel speedup is achieved through graph partitioning, speculative (iterative) coloring, and a BSP-like organization of computation. Experimental results show that the algorithm is scalable, and compares favorably with an alternative approach—solving the problem on a graph G by first constructing the square graph G 2 and then applying a parallel distance-1 coloring algorithm on G 2.

This work was supported in part by NSF grants ACI-0203722, ACI-0203846, ANI-0330612, CCF-0342615, CNS-0426241, NIH NIBIB BISTI P20EB000591, Ohio Board of Regents BRTTC BRTT02-0003, Ohio Supercomputing Center PAS0052, and SNL Doc.No: 283793. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin company, for the U.S. DOE’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

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Author information

Authors and Affiliations

  1. Ohio State University, USA
    Doruk Bozdağ, Umit Catalyurek & Füsun Özgüner
  2. Old Dominion University, USA
    Assefaw H. Gebremedhin
  3. University of Bergen, Norway
    Fredrik Manne
  4. Sandia National Laboratories, USA
    Erik G. Boman

Authors

  1. Doruk Bozdağ
  2. Umit Catalyurek
  3. Assefaw H. Gebremedhin
  4. Fredrik Manne
  5. Erik G. Boman
  6. Füsun Özgüner

Editor information

Editors and Affiliations

  1. Department of Computer Science, St. Francis Xavier University, Antigonish, Canada
    Laurence T. Yang
  2. School of Computer Science/Welsh eScience Centre, Cardiff University, UK
    Omer F. Rana
  3. Dipartimento di Ingegneria dell’ Informazione - Second, University of Naples - Italy, Real Casa dell’Annunziata - via Roma, 29 81031, Aversa (CE), Italy
    Beniamino Di Martino
  4. Computer Science Department, University of Tennessee, 37996-3450, Knoxville, TN, USA
    Jack Dongarra

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Bozdağ, D., Catalyurek, U., Gebremedhin, A.H., Manne, F., Boman, E.G., Özgüner, F. (2005). A Parallel Distance-2 Graph Coloring Algorithm for Distributed Memory Computers. In: Yang, L.T., Rana, O.F., Di Martino, B., Dongarra, J. (eds) High Performance Computing and Communications. HPCC 2005. Lecture Notes in Computer Science, vol 3726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11557654\_90

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